This study focuses on one of the most effective type of capacity markets named Capacity Subscription (CS) market which is predicted to be widely used in the upcoming smart grids. Despite variant researches done about the mechanism and structure of capacity markets, their performances have been rarely tested in the presence of network constraints. Considering this deficiency, we tried to propose a new method to determine capacity prices in the network considering the transmission line flow limitations named Local capacity Prices (LP). This method is quite new and has not been tried before in any other similar researches. The philosophy of the proposed method is to determine capacity prices considering each consumer share of total peak demand. The first advantage of LP is that the consumers who benefit from the transmission facilities and are the responsible for transmission congestions, pay higher capacity prices than those whom their needed electricity is prepared locally. The second advantage of LP is that consumers connected to the same bus do not have to pay same capacity price due to their different shares of total peak demand. For more clarification, two other different methods named Branches Flow limit as a Global Limit (BFGL) and Locational Capacity Prices (LCP) are proposed and compared to the LP method in order to show LP method efficiency. The numerical results obtained from case studies show that the LP method follows more justice market procedure which results in more efficient capacity prices in comparison to BFGL and LCP methods.